Blind compensation of polynomial mixtures of Gaussian signals with application in nonlinear blind source separation

In this paper, a proof is provided to show that Gaussian signals will lose their Gaussianity if they are passed through a polynomial of an order greater than 1. This can help in blind compensation of polynomial nonlinearities on Gaussian sources by forcing the output to follow a Gaussian distribution (the term “blind” refers to lack of any prior information about the nonlinear function). It may have many applications in different fields of nonlinear signal processing for removing the nonlinearity. Particularly, in nonlinear blind source separation, it can be used as a pre-processing step to transform the problem to a linear one, which is already well studied in the literature. This idea is proposed, proved, and finally verified by a simple simulation as a proof of concept in this paper.